All good enhancements played this battle may return to owner's hand except this one
It is very specific about where the cards end up for this card. It'd be the same as if you played Taking Egypt's Wealth, stole an enhancement from your opponent, and played it followed by Trust (or a similar card). It specifies "owner", that means...the owner. Whoever came to the game with that specific card in their deck.
You do have a case with Stillness (both versions), however:
"Hero may withdraw from battle unharmed. All enhancement cards played may be returned to the player's hand except this one."
In this case, it is all (both sides of the battle) enhancements, and as it says "player" instead of "owner, I'd posit that it was the player who used the enhancement who takes it to hand.
Of course, does redirecting a card also count as playing it, and would that lead to it returning to the redirecting player's hand?
All sorts of interesting questions.